Diversification measures: Mutual fund family case

Abstract

This study introduces a portfolio theory motivated approach to measuring mutual fund family-level risk diversification. The average cross-fund correlation in idiosyncratic returns measures diversification of idiosyncratic risk, while the correlation of predicted returns from the multifactor model measures factor risk diversification within a fund family. We document a substantial cross-sectional variation in family-level diversification measured with our new proxies independent of the number of funds and objectives in the family. While number of objectives is a popular yet possibly misleading measure of diversification, there is a link between portfolio theory-based diversification measures and the number of objectives in a family. On average, fund families with more investment objectives are more diversified in terms of both idiosyncratic and factor risks; yet, in large families, more investment objectives are associated with increased diversification of idiosyncratic risk but decreased diversification of factor risk. Fund family diversification improves family performance during market downturns and in large families. However, fund family diversification does not significantly affect absolute or relative family size, except for the number of investment objectives, which has a negative relation to family size.